The same is true for the music as long as it is "synchronized" with the film. The fact that the music is separately copyrighted means that you can't use the music separately just because the film is PD.

The story was originally written as a screenplay By Stone and Behm which was unpublished and unsold. The screenplay was adapted into a novel by Stone and published (serialised in magazine form). The film rights to this story were then purchased by Stanley Donen and a new screenplay was written by Stone. The film rights to the story and screenplay were then transferred to Universal Pictures. However, the copyright was retained by Peter Stone as reflected in the renewal for the copyright:

The problem with Charade is the same as It's A Wonderful Life.Charade is in the public domain while it's soundtrack isn't,so the only legal way Charade could be PD would be to remove the music,but I doubt that will happen.